A slicer is a device that determines a respective output data value or a respective output element of the output sequence as a function of an input data value or input element of the input sequence, a nominal input element being allocated to each possible output element. Determining the respective output element can be done by comparing the respective input element with one or more decision thresholds fixed depending on the nominal input elements.
Slicers of this kind are normally used when data are received via a transmission channel, in other words, for converting a received input sequence into an output sequence for further processing. Distortions may occur owing to the transmission of the input elements of the input sequence via the transmission channel, which may cause transmission errors. These distortions include, for example, inter-symbol interference (ISI), which leads to influencing of a current receiving element by preceding or optionally also following receiving elements. Equalizers are generally used to balance out distortions of this kind.
Decision feedback equalizers (DFE) are an example of equalizers of this kind. They are employed for equalizing transmission channels with strong inter-symbol interference, in particular if the implementation of a receiver on the basis of the principle of maximum likelihood sequence detection (MLSD) cannot be considered for reasons of complexity or dissipated power or owing to other peripheral conditions of the system, such as, for instance, the limitation of a maximum permissible latency. MLSD in principle offers better equalization. Linear equalizers are relatively easy to implement, for example on the basis of adaptive FIR filters, however noise increases with the strength of the inter-symbol interference. For strong inter-symbol interference, a decision feedback equalizer has less noise and a smaller length. Decision feedback equalizers of are frequently configured such that only a part of the inter-symbol interference which would lead particularly frequently to receiving errors is compensated, whereas weaker contributions are not compensated.
A simple decision feedback equalizer is schematically illustrated in FIG. 1. An analog input signal (receiving signal x) is fed to an analog-to-digital converter (ADC) 1. A sequence of receiving elements y is generated by the ADC 1, from which a respectively allocated correction value c is subtracted in a subtractor 2 to generate a respective differential value d. The sequence of differential values d is then fed to a slicer 3. Depending on the differential value d fed to it in each case, the slicer 3 determines an output symbol value ŷ (i.e. output signal), which in error-free transmission corresponds to a send symbol sent for generating the receiving signal x.
If a digital signal sequence is sent in which two possible values are represented by a positive value of the send symbol and a corresponding negative value of the respective send symbol of the signal sequence, the slicer 3 can compare the respective differential value d with a decision threshold of zero and at d>0 can output a value ŷ=1 and at d<0 a value ŷ=−1. The values +1 and −1 are here to be understood as examples; in principle any other pair of values suitable for the subsequent processing is also conceivable.
Each output symbol ŷ is fed to a delay element 7 and multiplied in a multiplier 11 by a coefficient c1 to generate the correction value c for the next input value y. Therefore, in the simple decision feedback equalizer illustrated, in each case the correction value c is determined for a receiving value y on the basis of the preceding output symbol value ŷ. By means of a decision feedback equalizer of this kind it is possible to compensate inter-symbol interference which originates from a receiving value preceding the current receiving value.
Frequently, there are several feedback paths of this kind with delay element and multiplier in decision feedback equalizers and the correction value c is generated by weighting and combination of several preceding output symbols ŷ to be able to correct the influence of several preceding receiving values to the current receiving value. However, these feedback paths are not necessary for understanding the present invention and have therefore not been illustrated for the sake of simplicity. The principle is in this case the same as with only one feedback path.
Furthermore, the respective output symbol ŷ is multiplied by a scaling factor c0 in a multiplier 9 and subtracted from the differential value d on the basis of which the output symbol value ŷ was determined in a subtractor 10 to form a decision error e. The scaling factor c0 is normally chosen such that with full equalization and otherwise undisturbed transmission the differential values d would correspond to the output symbol values ŷ multiplied by c0. If the differential values d, with undisturbed transmission and full compensation of the inter-symbol interference, had the possible values +h0 and −h0 and the output symbol values ŷ correspondingly the possible values +1 and −1, c0 would be set at h0. This means that the estimated error is e=0 if the differential value d coincides with the respective nominal differential value ±h0 in the case of perfect equalization and otherwise undisturbed transmission.
The estimated error e is used in operation of the decision feedback equalizer in particular to adapt the coefficient(s) of the equalizer, in the present example coefficient c1 to match the distortion properties to the transmission channel via which the analog receiving signal x is received, as its properties generally change over time. This can be done, for example, with a least mean square algorithm in which coefficient c1 is adapted according to:c1k+1=c1k+v·ek·sign(ŷk−1)  (1)
wherein v is a step width and k a running index, k=1, 2 . . . , which characterizes a respective element of the sequence of coefficients c1, of estimated errors e or of output symbols ŷ. An output symbol ŷk−1 preceding the estimated error ek is used for this, as the estimated error ek originating from the output symbol ŷk−1 is to be minimized.
To simplify the calculation of equation (1), instead of the estimated error ek, frequently only its sign is used. This is also illustrated in FIG. 1. Here a sign formation unit 8 forms the sign sek of the estimated error e. The adaptation of coefficient c1 is then carried out in an adaptation unit 32, for example, according to:c1k+1=c1k+v·sek·sign(ŷk−1)  (2).
If the output symbols ŷk adopt only values +1 and −1, sign (ŷk−1)=ŷk−1 applies, so there is no need to form the sign. In the decision feedback equalizer from FIG. 1, it is naturally also possible to scale the differential value d accordingly instead of the output symbol ŷ, to form the estimated error.
In FIG. 2, a further decision feedback equalizer is illustrated, which differs from the equalizer in FIG. 1 only in the way the estimated error e is determined. Therefore only this part of FIG. 2 is explained in greater detail; otherwise FIG. 2 corresponds to the already discussed FIG. 1.
In the equalizer of FIG. 2 the differential values d are fed not only to the slicer 3, but also to a positive input of a subtractor 5 and an input of an adder 4. A reference value a is fed to a negative input of the subtractor 5 and to a further input of the adder 4, so that a value e1=d−a and a value e2=d+a are generated. The values e1 and e2 are fed to a multiplexer 6, by which either value e1 or value e2 is selected as estimated error e, depending on the respective output symbol ŷ.
The reference value a corresponds in function to the scaling factor c0 from FIG. 1.
This will be explained again for the example where the output symbol ŷ can adopt the values +1 and −1 and the differential value d with undisturbed transmission and full compensation of inter-symbol interference, the values +h0 or −h0. For this case the reference value a is normally set at h0. Therefore e1=d−h0 and e2=d+h0 apply, corresponding exactly to the possible values for the estimated error. Correspondingly, e1 is selected by the multiplexer 6 as estimated error e for ŷ=+1 and e2 for ŷ=−1.
Decision feedback equalizers of this kind, as illustrated in FIG. 2, are useful in high speed applications, as the feedback of the output symbol ŷ into the subtractor 10 in FIG. 1 is time-critical, since it is here that the output symbol ŷ is subtracted from the differential value d as a function of which it was formed, to form the estimated error. On the other hand, in the look-ahead method of FIG. 2 such feedback is not present.
With the decision feedback equalizer from FIG. 2, the estimated error e (for example according to equation (1)) or its sign se (for example according to equation (2)) can also be used to adapt the coefficient c1. The use of the sign se again enables simpler implementation of the adaptation algorithm, as instead of multiplication only the sign (in digital implementation a corresponding sign bit) is altered.
However, if full compensation of inter-symbol interference does not occur, the problem discussed below may occur.
For this a pulse response of a transmission channel with a main value h0, a pre-pulse oscillator h−1 and a post-pulse oscillator h1 are illustrated in FIG. 3 by way of example. This means that a receiving element yk of the receiving sequence is calculated from a sent sequence bk, transmitted via the transmission channel, according to:yk=h1bk−1+h0bk+h−1bk+1  (3)
By means of decision feedback equalizers as shown in FIGS. 1 and 2, by suitable choice of the coefficient c1 the influence of the term h1bk−1 from equation (3), in other words the influence of the post-pulse oscillator h1, can be compensated, whereas the pre-pulse oscillator h−1 is not compensated.
If the adaptation process, as described with reference to equations (1) and (2), is carried out, this leads to the behavior illustrated schematically in FIG. 4. It has here been assumed that the bk from equation (3) can adopt only the values +1 and −1. For this case, in FIG. 4 curves 12 to 15 show possible values of the differential value d at the input of the slicer 3 of the decision feedback equalizers of FIGS. 1 and 2 over the time t. Initially a total of eight different values ±h0±h1±h−1 is possible, only the positive values (corresponding to ak=+1 in equation (3)) being illustrated. To calculate the decision error, as already explained, in FIG. 1 a scaling factor c0=h0 or in FIG. 2 a reference value a=h0 is used. In the course of the adaptation, the values d should from now on change according to the solid curves 12 to 15, so that after completion of the adaptation the two values h0+h−1 and h0−h−1 indicated by the dotted curves 30 and 31 result. In these values the influence of the post-pulse oscillator h1 is fully compensated.
According to equations (1) and (2) setting the coefficient c1 is done in proportion to the (signed) decision error or to its sign. If the sign algorithm from equation (2) is used, the problem now occurs that the sign changes its sign at the crossing point of curves 13 and 14 with h0. As only the sign and not the value of the estimated error is taken into account, the decision errors of curves 12 and 15 balance one another out on average and the setting of the equalizer coefficients remains constant on average. The values at the slicer input therefore emerge according to the dotted curves 16, 17 and 18 of FIG. 4. This is substantially because from the above mentioned crossing point onwards the influence of the pre-pulse oscillator h−1, which is not corrected, is ruling for the estimated error.
The minimum distance of these curves, in particular curve 16, from a slicer threshold x0=0 is less than in the optimum case, leading to an increased bit error rate.
Skilled artisans appreciate that elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale.